On unicyclic graphs of metric dimension 2 with vertices of degree 4
We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constr...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188412 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862552289047216128 |
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| author | Dudenko, M. Oliynyk, B. |
| author_facet | Dudenko, M. Oliynyk, B. |
| citation_txt | On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized.
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| first_indexed | 2025-11-25T21:04:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188412 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T21:04:25Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dudenko, M. Oliynyk, B. 2023-02-27T16:01:35Z 2023-02-27T16:01:35Z 2018 On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ. 1726-3255 2010 MSC: 05C12. https://nasplib.isofts.kiev.ua/handle/123456789/188412 We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized. The authors thank to the International Charitable Foundation for Renaissance of the Kyiv-Mohyla Academy for the financial support of their research. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On unicyclic graphs of metric dimension 2 with vertices of degree 4 Article published earlier |
| spellingShingle | On unicyclic graphs of metric dimension 2 with vertices of degree 4 Dudenko, M. Oliynyk, B. |
| title | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_full | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_fullStr | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_full_unstemmed | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_short | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_sort | on unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188412 |
| work_keys_str_mv | AT dudenkom onunicyclicgraphsofmetricdimension2withverticesofdegree4 AT oliynykb onunicyclicgraphsofmetricdimension2withverticesofdegree4 |